English

Estimation of large covariance matrices via free deconvolution: computational and statistical aspects

Probability 2023-05-10 v1 Statistics Theory Computation Statistics Theory

Abstract

The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical resolution of this problem. Our approach is based on complex-analytic methods methods to invert SS-transforms. In particular, one needs a theoretical understanding of the Riemann surfaces where multivalued SS transforms live and an efficient computational scheme.

Keywords

Cite

@article{arxiv.2305.05646,
  title  = {Estimation of large covariance matrices via free deconvolution: computational and statistical aspects},
  author = {Reda Chhaibi and Fabrice Gamboa and Slim Kammoun and Mauricio Velasco},
  journal= {arXiv preprint arXiv:2305.05646},
  year   = {2023}
}

Comments

v1: Preliminary version